From Lemma 2.1 of [1]} or [2]}, if \(0<\beta <\min \lbrace \mu _1,\mu _2\rbrace \)  or \(\beta >\max \lbrace \mu _1,\mu _2\rbrace \) , \((u_0,v_0)\)  is a least energy solution of (REF ), we have
\(J(u_0,v_0)=\frac{k_1+k_2}{4}\mathcal {S}^2 \ \ \text{and} \ \ \mathcal {S}_{\mu _1,\mu _2, \beta }=\sqrt{k_1+k_2}\mathcal {S}.\) 
